Category: Summaries
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Discussing “Sheaves in Geometry and Logic”
This is the second tome on topos theory I’ve read for this blog, but compared to The Elephant this one weighs in at a svelte 627 pages, and is a bit more approachable as a book to learn from, as opposed to an encyclopaedic reference. The conceit of The Elephant was that topoi can be…
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Discussing “Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic”
This is one of the classic papers – I’ve read, and cited, it a few times over the years myself – looking at extending the classic ‘Curry-Howard’ correspondence between lambda calculus and intuitionistic logic, to intuitionistic modal logic.
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Discussing “Basic Proof Theory”
The theory of logical proofs is divided, in this well-known textbook, into two strands: structural and interpretational.
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Discussing “Proof Analysis in Modal Logic”
Modal logics of necessity and possibility do not always obviously admit an acceptable notion of structural proof theory. Yet such systems can be invaluable for both work inside the logic (proof search) and work about a logic (metatheory). This paper looks at a general framework for defining sequent calculi for a wide range of classical…
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Discussing “An algebraic and Kripke-style approach to a certain extension of intuitionistic logic”
Heyting-Brouwer logic (more commonly known now as bi-intuitionistic logic) has fascinated me since I first learned of it. The idea is beguilingly simple: extend intuitionistic logic with a new connective that makes it completely symmetrical. The ‘symmetry’ I am thinking of (perhaps better called ‘duality’, but not quite the same thing as De Morgan duality)…
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Discussing “A very modal model of a modern, major, general type system”
This paper is an influential landmark in the development of what is now usually called guarded recursion, following a trail that roughly goes from Nakano’s introduction of the approximation modality, to this paper, to a Dreyer, Ahmed, and Birkedal paper that I haven’t yet read for this blog but will probably eventually get to, to…
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Discussing “The MetaCoq Project”
I’ve written before about Coq, recently renamed to Rocq, a proof assistant based on Martin-Löf’s dependent type theory. This paper, along with various sequels written in the six years since the project was first announced, aims to mechanise the syntax and semantics of Rocq, in Rocq.
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Discussing “First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory”
I’ve been meaning to get more familiar with this dissertation for a while (reading it thoroughly would take longer than the week I try to take for my blog posts), after its ideas were used in a paper I discussed last year. This thesis presents a new technique, synthetic Tait computability, for proving the ‘syntactic’…
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Discussing “Nested Sequents for Intuitionistic Logics”
About a year and a half ago I wrote about hypersequents, a modification of the tried and trusted sequent calculus approach to structural proof theory. In that setting, instead of working with a single sequent (a set of premises alongside a set of possible conclusions) we work with a list of sequents. In this paper,…
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Discussing “Modal Logic”
I learned modal logic from a book by Hughes and Cresswell, a pair of philosophers from my home city of Wellington, so it was interesting for me to see the very different approach taken in this week’s book, which is now the standard reference for the field ( along with the Chargrov- Zakharyaschev book of…
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Recent Posts
- Discussing “Sheaves in Geometry and Logic”
- Discussing “Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic”
- Discussing “Basic Proof Theory”
- A Blog Update for 2025
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1994 1996 2000 2001 2014 2019 2020 2021 2023 Abhishek Anand Cambridge Tracts in Theoretical Computer Science Carnegie Mellon University City University of New York Coq Cubical Type Theory Cyril Cohen Eike Ritter Fabian Kunze intuitionistic logic intuitionistic modal logic Jonathan Sterling Journal of Automated Reasoning LICS LORIA Matthieu Sozeau Melvin Fitting Metaprogramming modal logic nested sequent calculus Nicolas Tabareau Notre Dame Journal of Formal Logic Proof theory Rocq sequent calculus Simon Boulier Théo Winterhalter types type theory University of Amsterdam University of Birmingham University of Cambridge University of Oxford Valeria de Paiva Yannick Forster Yde Venema